%% term_Uold_grad_W_Psi
function matrix_A = term_Uold_grad_W_Psi(mesh, fespace, Uold)
Nb = fespace.Nb;
Nlb = fespace.Nlb;
rows = zeros(mesh.Ne*Nlb*Nlb,1);
cols = rows;
val1 = rows;
flag = 1;
for n = 1:mesh.Ne
    V = mesh.node(mesh.elem(n,:),:);
    [int_points_loc, int_weights_loc] = integral_loc(V, "2d");
    phi = basis_loc(V, int_points_loc(:,1), int_points_loc(:,2), fespace.basis_type, "x");
    phix = basis_loc(V, int_points_loc(:,1), int_points_loc(:,2), fespace.basis_type, "dx");
    phiy = basis_loc(V, int_points_loc(:,1), int_points_loc(:,2), fespace.basis_type, "dy");
    u1 = phi * Uold(fespace.elem(n,:),:);
    u2 = phi * Uold(fespace.elem(n,:)+Nb,:);
    for i = 1:Nlb
        for j = 1:Nlb
            f1 = u1.*phix(:,j).*phi(:,i) + u2.*phiy(:,j).*phi(:,i);
            r1 = int_weights_loc * f1;
            rows(flag) = fespace.elem(n,i);
            cols(flag) = fespace.elem(n,j);
            val1(flag) = r1;
            flag = flag + 1;
        end
    end
end
matrix_A = sparse(rows, cols, val1, Nb, Nb);
end